According to local government officials, at least three rockets landed on Information & Culture Directorate, provincial municipality and Museum compounds.
Deputy provincial governor Mohammad Ali Ahmadi confirmed the incident and said sporadic gun fires are also heard in the vicinity of Ghazni city.
There are no reports regarding the casualties as a result of the rocket attack and sporadic clashes.
The Taliban militants group claimed responsibility behind the rocket attacks and claimed that heavy casualties were incurred as a result of the attack.
Ghazni is among the relatively volatile provinces in southeastern Afghanistan where anti-government armed militant groups are actively operating and frequently carry out insurgency activities.